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24 Nov 2021, 07:00
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (01:41) correct
28%
(01:25)
wrong
based on 92
sessions
History
Date
Time
Result
Not Attempted Yet
If AB = 5cm, is the perimeter △ABC > 20cm?
(1) BC = 13cm
(2) 10cm < AC < 13cm
(1) BC = 13cm
(2) 10cm < AC < 13cm
24 Nov 2021, 07:21
Kudos
Bookmarks
If one side of the triangle is 5 units long, and if another side is more than 10 units long, the third side will definitely need to be more than 5 units long because the sum of the lengths of any two sides of a triangle must exceed the third. So using either statement the perimeter exceeds 20 and the answer is D.
14 Apr 2023, 05:35
Kudos
Bookmarks
Bunuel
Solution:
Pre Analysis:
- Side \(AB=5\) cm
- We are asked if perimeter of \(△ABC > 20\) cm
Statement 1: BC = 13cm
- We have 2 sides and the range of third side AC will be
- \(13-5<AC<13+5\)
- Or \(8<AC<18\)
- So, \(AB=5, BC=13\) and \(AC>8\) and the perimeter will be greater than 5 + 13 + 8 or \(perimeter>26\)
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: 10cm < AC < 13cm
- \(AB=5\) and \(AC>10\)
- Third side \(BC>10-5\) or \(BC>5\)
- So, \(AB=5, BC>5\) and \(AC>10\) and the perimeter will be greater than 5 + 5 + 10 or \(perimeter>20\)
- Thus, statement 2 alone is also sufficient
Hence the right answer is Option D
